They end within a few miles of each other. and line up perfectly. An extension of OK 31 to the AR line would create a single corridor. To connect these highways, you either have to go way out of the way or to travel a county road.
Looks to me like the reasoning is environmental- there's a pretty big chunk of riparian corridor through there, and besides being an isolated chunk of habitat in a developed area, it looks like it serves as a pretty important rainwater sink for the surrounding area, so probably not something you want to develop in unless you want the surrounding farms a lot more susceptible to flooding.
You could certainly build a road that accommodates for all of that, but it wouldn't be cheap, and I'm guessing there's not enough traffic on 31/10 that isn't interacting with Spiro in some way to justify it.